Hello.
In the local store, they only had the IRFP360 (Rdson 0.2 Ohm) in a TO247 package and a 330uH/0.5 Ohm coil. I bought them for tests.
I replaced the coil first, but the result was not quite good.
After replacing the MOSFET, great results came. HV will run at 180V much faster than before (a few seconds). It is held stably and the PWRontime calibration ended with a result of 178. And most importantly the temperature dropped to 32 degrees (measured using a contact PT100 probe). I can also use a 9V power supply without any problems.

Finally, I returned the original 100uH/0.2Ohm coil to see what it would do. It works. MOSFET temperature slightly higher, HV less stable and longer PWRontime.
I'll look for suitable replacements for the MOSFET and do other tests with 150-220uH coils, which will probably be better.
I'll write the results here, maybe it will help someone in the future.
Vladca